How did our human ancestors evolve to have better medicine adsorption under the tongue?

You have it backwards.

The underside of the tongue does not need particularly thick skin as it's not normally in contact with possibly abrasive materials in food.

It also needs to be extremely flexible to allow the tongue the maximum movement within the mouth.

And the blood vessels that supply the tongue are least likely to be damaged if away from the top surface of the tongue; towards the underside.

Add those together and you get an area with particularly thin and elastic skin over an area rich in blood vessels.

Doctors and drug developers simply taking advantage of that fact.

https://chembam.com/definitions/adsorption-vs-abso... 

I'm not going to give you a specific answer, because what's needed here is a more basic, fundamental tutorial on how evolution works, and how it doesn't work:  You ought to be able to apply this information to the specific question you're asking.

1) Traits do NOT evolve according to some supposed need or design goal. 

2) As a mechanism, selection does NOT anticipate future possible need or advantage; rather, it occurs based on whether a given trait--whatever it is--helps or hinders a population's ability to reproduce under existing environmental conditions.  And that's it.

3) Just because a particular trait exists now, does NOT necessarily mean that it was specifically selected for.  Some traits persist simply because they don't hurt anything.  Others last because they may "tag along" for the ride, alongside other, more critical traits which HAVE BEEN under selective pressure.  Strict adaptationism, i.e. the notion that EVERYTHING we now have was specifically "selected for" has been pretty much abandoned by biologists.  And for good reason.

Not just humans. Sweet, bitter, and umami tastes are detected by way of G protein-coupled taste receptors. G protein-coupled receptors are found only in eukaryotes, including yeast, choanoflagellates, and animals. G protein-linked receptors (GPLR), form a large group of evolutionarily-related proteins that are cell surface receptors that detect molecules outside the cell and activate cellular responses. GPCRs are an important drug target and approximately 34% of all Food and Drug Administration (FDA) approved drugs target 108 members of this family.

Your question is a load of nonsense.

We did not evolve a special mechanism for dissolving medicines under the tongue.

The medicines are designed to dissolve in the moisture found inside the mouth. The mouth is lined with mucous membranes. Mucous membranes can and do absorb substances.

That is why drugs can be given in suppositories (put into the anus) and pessaries (put into the vagina). They dissolve because of the body's warmth and moisture and because these areas are lined with mucous membranes they are absorbed.

You would need a lot more proof of went on 500,000 years ago.